Pension reform, employment by age, and long-run growth in OECD countries.

Transcription

1 FACULTEIT ECONOMIE EN BEDRIJFSKUNDE TWEEKERKENSTRAAT 2 B-9000 GENT Tel. : 2 - (0) Fax. : 2 - (0) WORKING PAPER Pension reform, employmen by age, and long-run growh in OECD counries. Tim Buyse 1, Freddy Heylen 1,2 and Renaa Van de Kerckhove 1 1 SHERPPA, Ghen Universiy, 2 IRES, Universié caholique de Louvain May /719 Paper presened a he 10h Journées d'economie Publique Louis-André Gérard-Vare, Marseille, June 2011, and he 2011 Annual Meeing of he Sociey for Economic Dynamics, Ghen, July D/2011/7012/24

2 Pension reform, employmen by age, and long-run growh in OECD counries Tim Buyse 1, Freddy Heylen 1,2 and Renaa Van de Kerckhove 1 1 SHERPPA, Ghen Universiy, 2 IRES, Universié caholique de Louvain May 2011 Absrac We sudy he effecs of pension reform in a four-period OLG model for an open economy where hours worked by hree acive generaions, educaion of he young, he reiremen decision of older workers, and aggregae per capia growh, are all endogenous. Nex o he characerisics of he pension sysem, our model assigns an imporan role o he composiion of fiscal policy. We find ha he model explains he facs remarkably well for many OECD counries. Our simulaion resuls prefer an inelligen pay-as-you-go pension sysem above a fully-funded privae sysem. When i comes o promoing employmen, human capial, growh, and welfare, posiive effecs in a PAYG sysem are he sronges when i includes a igh link beween individual labor income (and conribuions) and he pension, and when i aaches a high weigh o labor income earned as an older worker o compue he pension assessmen base. Key words: employmen by age, endogenous growh, reiremen, pension reform, overlapping generaions JEL Classificaion: E62, H55, J22, O41 Correspondence o Tim.Buyse@UGen.be, Freddy.Heylen@UGen.be or Renaa.Vandekerckhove@UGen.be. Sherppa, Ghen Universiy, Tweekerkensraa 2, B-9000 Ghen, Belgium, Phone We hank David de la Croix, Fabian Kindermann, Dirk Van de gaer and Geer Vancronenburg for consrucive commens and discussions during he developmen of his paper. We have also benefied from commens received a he 29h Flemish Scienific Economic Conference (November 2010), he UAP Day on Economic Policy and Finance in he Global Economy: Equilibrium Analysis and Social Evaluaion (Ghen, December 2010), he 2011 OLG Days (Vielsalm, May 2011) and seminars in Brussels and Louvain. We acknowledge suppor from he Flemish governmen (Seunpun Fiscaliei en Begroing - Vlaanderen) and he Belgian Program on Ineruniversiy Poles of Aracion, iniiaed by he Belgian Sae, Federal Office for scienific, echnical and culural affairs, conrac UAP No. P 6/07. Any remaining errors are ours.

3 1. Inroducion Concern for he long-run financial viabiliy of public pension sysems has pu pension reform high on he agenda of policy makers and researchers. The pas wo decades have seen a wave of reforms in many counries (Whiehouse e al., 2009). A he same ime he lieraure on pension economics has grown rapidly (see e.g. Lindbeck and Persson, 200; Fenge and Pesieau, 2005; Barr, 2006; and many recen papers ha we refer o below). To face he pension challenge, here seems o be general agreemen on he need for higher employmen, especially among older individuals, and higher produciviy growh. Many sudies have documened how he pension sysem may affec he incenives of individuals of differen ages o work (e.g. Auerbach e al., 1989; Gruber and Wise, 2002; Cremer e al., 2008; Sánchez Marín, 2010; Börsch-Supan and Ludwig, 2010; Fisher and Keuschnigg, 2010; Jaag e al., 2010; de la Croix e al., 2010). Ohers have invesigaed he relaionship beween he pension sysem and invesmen in human capial formaion, as a major deerminan of produciviy growh (e.g. Zhang, 1995; Kemniz and Wigger, 2000; Docquier and Paddison, 200; Zhang and Zhang, 200; Le Garrec, 2011). Sill ohers have demonsraed he crucial role of human capial formaion o counerac he negaive effecs of populaion ageing on per capia oupu (e.g. Docquier and Michel, 1999; Fougère e al., 2009; Ludwig e al., 2010). Consensus on wha pension reform would serve he goals of higher employmen, produciviy growh and welfare bes, has however no been reached. Policy recommendaions vary from parameric adjusmens in he pay-as-you-go (PAYG) sysem ha mos counries rely on, o a gradual move o an acuarially neural fully-funded privae sysem. Ofen, differences in he paricular specificaion of he model economy ha is used for he analysis may explain differences in policy conclusions. In his paper we consruc and parameerize a general equilibrium four-period OLG model for an open economy. The model explains hours of work of young, middle-aged and older individuals, educaion and human capial formaion of he young, he reiremen decision of he older generaion, and aggregae per capia growh. I includes a public PAYG old-age pension sysem which pays ou pensions o a fourh generaion of reired. The sauory reiremen age in our model is 65 and exogenous. Old-age pensions are paid from his age onwards. Individuals, however, may opimally choose a lower effecive (early) reiremen age. The governmen in he model ses ax raes on labor, capial and consumpion. I allocaes is revenue o producive expendiures (mainly for educaion), consumpion, non-employmen benefis (including early reiremen benefis) and old-age pension benefis. Our aim is o invesigae he effecs of various parameric adjusmens in he early reiremen regime and in he old-age PAYG pension sysem. These parameric adjusmens include changes in benefi levels, changes in he link beween benefis and individual conribuions, and changes in he weighs of he hree acive periods in he compuaion of he old-age pension assessmen base, i.e. earned labor income used o calculae pension benefis. We also consider he effecs of moving o full privae capial funding. Our main conribuion in his paper is o sudy he impac of pension sysems on employmen by age, he effecive reiremen decision, educaion and growh, and he welfare of curren and fuure generaions wihin one coheren framework, where all hese variables are endogenous. Here we differ from he exising lieraure. The above menioned sudies eiher invesigae incenives o work in a model wih exogenous human capial and growh, or invesigae human capial and growh while 2

4 ignoring he labor-leisure choice and he endogeneiy of labor supply 1. Our approach allows o fully ake ino accoun he muual relaionships beween all variables, which will maer for he size and possibly he direcion of policy effecs. Various channels exis in our model whereby he effecs of changes in employmen and changes in capial formaion reinforce each oher. For example, if employmen rises, so will he marginal produciviy of physical capial and he incenive o inves. Also, if people pospone reiremen and work longer, he reurn o invesmen in educaion will rise, and so may human capial and growh. Conversely, policies ha promoe educaion will encourage people o work longer since hey will hen ge a higher reurn from heir invesmen. Our model also conains channels where employmen and growh will move in opposie direcions. One channel follows from he possible radeoff beween employmen of he young and educaion. Pension reform which discourages employmen of he young may sill be posiive if his conribues o educaion and growh. As we show in his paper, he final effecs of pension reform depend on all hese ineracions. I will be imporan o have a realisic esimae of key parameers, for example in he specificaion of he human capial producion funcion, or in labor supply by age. Nex o he endogeneiy of all key variables, our model conains a number of oher feaures which maer for he analysis of he effecs of pension reform, bu which are ofen ignored in he lieraure. The mos imporan of hese is a realisic modeling of he ransiion from work o reiremen, and he role of early reiremen regimes. These regimes play an imporan role in many counries. We explicily disinguish he effecive (early) reiremen age, which is opimally chosen, and he sauory reiremen age, which is exogenous (see also Heijdra and Romp, 2009; de la Croix e al., 2010). Old-age pensions in our model are paid only from he sauory reiremen age onwards. A key implicaion is ha old-age pensions do no direcly raise he opporuniy cos of working in our model. Early reiremen benefis do. In he lieraure his disincion is ofen no made (e.g. Hu, 1979; Börsch-Supan e al., 2006; Jaag e al., 2010; Fisher and Keuschnigg, 2010). I may obviously affec he evaluaion of old-age pension reform. As a second feaure, we allow individual pension benefis in he PAYG sysem o depend on accumulaed individual labor income and conribuions, raher han on average per capia labor income. Many counries have iniiaed reforms ha srenghen his individual conribuions - benefi link. Lindbeck and Persson (200), Zhang and Zhang (200) and Jaag e al. (2010) demonsrae he imporance of aking his link ino accoun. Ohers however ignore i when modeling a PAYG sysem, which may oversae he disorion induced by his sysem (e.g. Börsch-Supan and Ludwig, 2010; Ludwig e al., 2010) 2. Anoher characerisic which affecs our resuls, is he assumpion of an open economy. I has been shown ha pension reform may have profound effecs on inernaional capial flows (e.g. Börsch-Supan e al., 2006). In an open economy, changes in naional savings need no feed hrough ino invesmen in he domesic economy. Facor price changes may be much weaker han presumed in closed economy models. Clearly, his may affec employmen and human capial formaion. As a final feaure, we assume ha demography and populaion are consan in our model. Alhough ageing is obviously a crucial facor behind pension reform in many counries, his assumpion need no be a limiaion o disenangle behavioral effecs from pension reform (see also Jaag e al., 2010; Fisher and Keuschnigg, 2010). 1 Fougère e al. (2009) and Ludwig e al. (2010) also develop a model wih endogenous employmen by age and human capial, bu hey have exogenous growh. Moreover, Fougère e al. (2009) do no sudy pension reform. 2 Long ago, Sheshinski (1978) already showed in a model ha a pension sysem can encourage work and lae reiremen if benefis increase in he reiremen dae. This idea has been picked up also by Gruber and Wise (2002).

5 To sudy he effecs of pension reform we parameerize, numerically solve, and simulae our model. Before we do ha, however, we es is empirical validiy for a group of 1 OECD counries. The counries ha we consider include he US, he core counries of he euro area, he UK, Canada and he Nordic counries. Our main moivaion for his es goes back o Sokey and Rebelo (1995), who find exreme variaion in he predicions of exising calibraed models invesigaing he effecs of public policy in he lieraure. Before using a parameerized heoreical model for policy simulaions, we would herefore like o ge a leas some minimal evidence ha he model s predicions are wihin reliable bands. Our procedure is as follows. We impose common echnology and preference parameers on all counries, bu counry-specific fiscal policy and pension sysem parameers. Simulaing he model for each counry we find ha is predicions mach he main facs in mos counries. These facs concern observed hours of work in hree age groups (20-4, 5-49, 50-64), educaion of he young (20-4), he effecive reiremen age, and per capia growh since We conclude ha he model ranslaes observable policy differences ino performance differences which are roughly in line wih observaions in he daa. Having esablished is empirical reliabiliy, we hen use he model for policy simulaions. Our simulaions assess o wha exen pension reform may conribue o employmen, growh and welfare. Our resuls speak in favor of an inelligen PAYG sysem. This sysem conains a close link beween old-age pensions and individual labor earnings and conribuions via a high pension replacemen rae. Even more imporan is a high weigh of labor income (i.e. hours worked and human capial) earned as an older worker in he pension assessmen base. Pension reform in his direcion encourages young individuals o sudy and build human capial, which promoes long-run growh. Furhermore, i encourages older workers o pospone reiremen. Srenghening he link beween one s fuure old-age pension, on he one hand, and one s human capial and labor supply when older, on he oher, inroduces srong financial incenives which may bring abou imporan changes in behavior. Posiive effecs on employmen, he effecive reiremen age, and growh, raise he governmen s resources, which makes i possible o finance a larger pension burden. Our resuls prefer a reform of he PAYG sysem along hese lines above a movemen o a fully funded privae sysem, boh from he perspecive of employmen, growh and welfare. We demonsrae he imporance of he paricular characerisics in our model ha we have emphasized above. Finally, whereas our resuls show ha old-age pension benefis may rise in an inelligen PAYG sysem, early reiremen benefis mus be reduced. This paper confirms ha he pension sysem can be a valuable policy insrumen in is own righ, as recenly emphasized also by Cigno (2010). When i comes o employmen, our resuls are in line wih argumens for a change of he rules in acuarial direcion as explained by Gruber and Wise (2002), Lindbeck and Persson (200) and Cigno (2010) among ohers. Furhermore, our resuls demonsrae he imporance of also aking ino accoun possible effecs on educaion, human capial and growh. The srucure of his paper is as follows. In Secion 2 we documen differences in employmen by age, educaion of he young, he effecive reiremen age, and per capia growh across 1 OECD counries since Secion ses ou our model. In Secion 4 we calibrae he model on acual daa and confron is predicions wih he facs described in Secion 2. Secion 5 includes he resuls of a range of model simulaions. We invesigae he seady sae effecs of various reforms of he pension sysem. We also sudy ransiional dynamics, and he welfare effecs per generaion. Secion 6 concludes he paper. 4

6 2. Cross-counry differences in employmen by age, eriary educaion and per capia growh Table 1 conains key daa on employmen, educaion and growh in 1 OECD counries in One would like a reliable model o mach he main cross-counry differences repored here. The employmen rae in hours (n) indicaes he fracion of poenial hours ha are acually being worked by he average person in one of hree age groups (20-4, 5-49, 50-64). Poenial hours are 2080 per person per year (52 weeks imes 40 hours per week). The observed employmen rae rises if more people in an age group have a job, and if he employed work more hours. The employmen rae in he age group of 50 o 64 is also affeced by he average age a which older workers wihdraw from he labor force. We also include he effecive reiremen age in Table 1. In mos counries, his age is well below he official age o receive old-age pensions (65 in mos counries, 60 in France). The educaion rae (e) is our proxy for he fracion of ime spen sudying by he average person of age I has been calculaed as he oal number of sudens in full-ime equivalens, divided by oal populaion in his age group. Our daa for (average annual) real per capia growh concern real poenial GDP per person of working age. We refer o Appendix 1 for furher deails on he calculaion of all our daa, and on he assumpions ha we have o make. Table 1 Employmen rae in hours (n), effecive reiremen age, educaion rae (e) and per capia growh in OECD counries ( /7) n 1 (20-4) n 2 (5-49) n (50-64) Effecive reiremen age e Annual real per capia growh Ausria Belgium France Germany Ialy Neherlands Core euro area Average Denmark Finland Norway Sweden Nordic Average US UK Canada All counry average Daa sources: OECD (see Appendix 1); daa descripion: see main ex and Appendix 1. The daa for employmen and growh concern , hose for educaion The effecive reiremen age is an average for All daa are in percen, excep he reiremen age. 5

7 As is well-known, middle-aged individuals work mos hours, followed by he young. The older generaion works he lowes number of hours. Average employmen raes over all counries in hese hree age groups are 55.0%, 6.7% and 4.6% respecively. Furhermore, he daa reveal srong cross-counry differences. We observe he highes employmen raes in each age group in he US. Employmen raes are much lower in he core counries of he euro area. The Nordic counries ake inermediae posiions, alhough hey are close o he core euro area for he younger generaion. The laer, however, seems o be relaed o educaion. Young people s paricipaion in educaion is by far he highes in he Nordic counries. These counries also show he highes poenial per capia growh raes. On average, growh in he core euro area and he US was more han 0.5 percenage poins lower in he period under consideraion. The US and he oher Anglo-Saxon counries end o have he lowes paricipaion in educaion among people of age 20 o 4. Finally, we noe ha he effecive reiremen age also varies across counries. The reiremen age is quie low in Belgium (57.9) and France (58.8). By conras, individuals in Nordic or Anglo-Saxon counries paricipae longer. Unsurprisingly, correlaion beween he effecive reiremen age and he employmen rae among older workers (n ) is very high (0.89).. The model Our analyical framework consiss of a compuable four-period OLG model for a small open economy. We assume perfec inernaional mobiliy of physical capial bu immobile labor and human capial. Seminal work in he OLG radiion has been done by Samuelson (1958) and Diamond (1965). Auerbach and Kolikoff (1987) iniiaed he sudy of public finance shocks in a compuable OLG model. Buier and Klezer (199) developed an open economy version of he model wih endogenous growh, puing human capial a he cenre. As we have documened in Secion 1, a huge lieraure has used OLG models o sudy he behavioral effecs of he pension sysem, eiher on employmen, assuming exogenous growh, or on human capial and growh, assuming exogenous employmen. New in our model is ha employmen by age, educaion and human capial, and growh, are joinly endogenous. We consider hree acive adul generaions, he young, he middle-aged and he older, and one generaion of reired agens. All generaions are of equal size, normalized o 1. Populaion is consan. Wihin each generaion agens are homogeneous. Individuals ener he model a age 20. Each period is modeled o las for 15 years. Young people can choose eiher o work and generae labor income, o sudy and build human capial, or o devoe ime o leisure (including oher nonmarke aciviies). Middle-aged and older workers do no sudy anymore, hey only work or have leisure. The sauory old-age reiremen age is 65. Individuals may however opimally choose o leave he labor force sooner in a regime of early reiremen. Domesic firms ac compeiively and employ physical capial ogeher wih exising echnology and effecive labor provided by he hree acive generaions. A final imporan assumpion is ha educaion generaes a posiive exernaliy in he sense of Azariadis and Drazen (1990). The average level of human capial of a middle-aged generaion is inheried by he nex young generaion. In wha follows, we concenrae on he core elemens of he model: he opimizing behavior of individuals, he producion of effecive human capial, he behavior of domesic firms and he deerminaion of aggregae oupu and growh, capial and wages. 6

8 .1. Individuals An individual reaching age 20 in maximizes an ineremporal uiliy funcion of he form: u 1 θ l j = + γ (1) j 1 θ 4 j 1 β ln c j j = 1 wih γ j >0, θ >0 (θ 1) and where: l (2) 1 = 1 n 1 e 2 = 1 n2 l () l and l 1 ( 1/ ρ ) ɶ = Ω π ( R ( 1 n )) + ( 1 π )( 1 R ) 4 = 1 1 ( 1/ ρ ) ρ / ( ρ 1 ) (4) Lifeime uiliy (1) depends on consumpion (c j ) and enjoyed leisure (l j ) in each period of life. Superscrip indicaes he period of youh, when he individual comes ino he model. Subscrip j refers o he jh period of life. Furhermore, β is he discoun facor (0<β<1). The ineremporal elasiciy of subsiuion in consumpion is 1, he ineremporal elasiciy o subsiue leisure 1/θ. Finally, γ specifies he relaive value of leisure versus consumpion. Noe ha γ may be differen in each period of life. Excep for he laer assumpion, our specificaion of he insananeous uiliy funcion is quie common in he macro lieraure (e.g. Benhabib and Farmer, 1994; Rogerson, 2007). Figure 1 shows he life-cycle of an individual reaching age 20 in. Individuals choose ime devoed o work (n j ) in he hree acive periods and educaion ime (e 1 ) when young. Since individuals only allocae ime o educaion in heir firs period, we drop he subscrip 1 in wha follows. Time endowmen is normalized o 1 in each period. The deerminaion of early reiremen is par of individuals opimal choice of leisure ime in he hird period of life (50-65). Individuals choose R which relaes o he opimal effecive reiremen age and which is defined as he fracion of ime beween age 50 and 65 ha he individual paricipaes in he labor marke; (1-R) is hen ime in early reiremen. We use n o denoe he fracion of ime devoed o work beween 50 and 65, and as he fracion of ime devoed o work before early reiremen, bu afer 50. As labor marke exi is irreversible and pos-reiremen employmen is no allowed in our model, he relaionship beween n and is as follows: n =.. In he firs wo periods of acive life, leisure falls in labor supply and in educaion ime (Equaions 2 and ). In he hird period, leisure ime consiss of wo pars: non-employmen ime before he effecive reiremen age ( (1, and ime in early reiremen afer i (1-R). Equaion (4) hen describes composie enjoyed leisure of an older worker as a CES-funcion of boh pars. We assume imperfec subsiuabiliy beween he wo leisure ypes. The idea here is ha leisure ime afer and beween periods of work is no he same as leisure ime in periods when individuals are 7

9 no economically acive anymore. Equaion (4) expresses ha individuals prefer o have a balanced combinaion of boh raher han an exreme amoun of one of hem (and very lile of he oher). In his equaion ρ is he consan elasiciy of subsiuion, π is a usual share parameer and Ω is added as a normalizaion consan such ha he magniude of l corresponds o he magniude of oal leisure ime 1-n. 4 The laer assumpion allows o inerpre γ as he relaive value of leisure versus consumpion in he hird period, comparable o γ 1 and γ 2. Figure 1. Life-cycle of an individual of generaion R Period Work = 0 Sudy Leisure ime 1 1 (1 +(1 1 Individuals will choose consumpion, labor supply, educaion and heir effecive reiremen age o maximize Equaion (1), subjec o Equaions (2)-(4) and he consrains described in (5)-(12). c ( 1 + τ )c + a = w h n ( 1 τ ) + b w h ( 1 τ )( 1 n e ) + z (5) c ( 1+ τ )c + a = w h n ( 1 τ ) + b w h ( 1 τ )( 1 n ) + ( 1+ r )a + z ( 1+ τ )c + a = w h n ɶ ( 1 τ ) + b w h ( 1 τ )R n ɶ ) c + 2 R a + 2 ( 1 τ c ( 1+ )c = ( 1+ r )a + pp + z b τ 1 ) ( 1 r + 2 )a 2+z b w h ( )( R + + (6) (7) (8) 1 wih: h1 = h 2 (9) ( 1 y ) 2 1 h = h = + ψ ( e,g,q ) h ψ >0, ψ'(.)>0 (10) j + 4 j and: pp4 = b4a p jw + j 1hjn j( 1 τ j ) x+ i 1 + b4b ( w + hj n j ( 1 τ j )) j= 1 i= j j= 1 (11) The former may be paricularly valuable from he perspecive of relaxaion and ime o spend on personal aciviies of shor duraion. The laer may be valuable o enjoy aciviies which ake more ime and ask for longer erm commimen (e.g. long journeys, non-marke aciviy as a voluneer). 4 The resuls in his paper are no in any way influenced by he magniude of π, Ω or ρ (see Secion 4.1.). 8

10 wih : 0 p 1, j= 1 j p = 1, j x = 1+ ψ( e,g y,q ), and n = R nɶ (12) The LHS of Equaions (5)-(8) shows ha individuals allocae heir disposable income o consumpion (including consumpion axes, τ c ) and he accumulaion of non-human wealh a. We denoe by he sock of wealh ha an individual who eners he model a ime holds a he end of his jh period of life. During he hree periods of acive life disposable income a he RHS includes afer-ax labor income, non-employmen benefis, ineres income and lump sum ransfers. In each equaion, w k sands for he real wage per uni of effecive labor a ime k, r k is he exogenous (world) real ineres rae a ime k, and z k is he lump sum ransfer ha he governmen pays ou o all individuals a ime k. Effecive labor of an individual depends on hours worked ( ) and effecive human capial (h ). Since young individuals allocae a fracion of heir ime o work, and pay a ax rae on labor income τ 1, hey earn an afer-ax real wage equal o w h1 n 1( 1 τ1 ). Afer-ax labor income of middle-aged and older workers in equaions (6) and (7) is deermined similarly. A young worker inheris his effecive human capial from he middle-aged generaion, as shown in Equaion (9). During he second and hird period, workers supply more unis of effecive human capial. I is our assumpion in Equaion (10) ha h rises in educaion ime when young (e), producive governmen spending in percen of GDP (g y, mainly educaion) and he qualiy of educaion (q). We specify and discuss he effecive human capial producion funcion in Secion.2. Individuals ake g y and q as exogenous. We assume ha human capial remains unchanged beween he second and hird period. We have in mind ha learning by doing in work may counerac depreciaion. For he fracion of ime ha young, middle-aged and older individuals are inacive, hey receive a non-employmen benefi from he governmen. Older workers may be eligible o wo kinds of benefis: sandard non-employmen benefis (analogous o wha young and middle-aged workers receive) as long as hey are on he labor marke, and early reiremen benefis afer having wihdrawn from he labor marke. All benefis are defined as a proporion of he afer-ax wage of a full-ime worker. The replacemen rae for sandard non-employmen benefis is b j wih j=1,2,a, for early reiremen benefis i is b b. 5 Afer he sauory reiremen age (65) individuals have no labor income and no non-employmen benefis anymore. They hen receive an old-age pension benefi (pp) and he lump sum ransfer. Equaion (11) describes he old-age pension. We assume a public PAYG pension sysem in which pensions in period k are financed by conribuions (labor axes) from he acive generaions in ha period k (see below). Individual ne pension benefis consis of wo a j 5 Our approach o model early reiremen benefis as a funcion of a worker s las labor income, similar o sandard non-employmen benefis, reflecs regulaion and/or common pracice in many counries. In some counries (e.g. Belgium, he Neherlands) workers can ener he early reiremen regime only from employmen, wih heir benefis being linked o he las wage. In oher counries (e.g. Denmark) here is only access from unemploymen, wih he early reiremen benefi being linked o he unemploymen benefi (Salomäki, 200). As o common pracice, Duval (200) confirms ha in many counries, unemploymenrelaed or disabiliy benefis can be used de faco o bridge he ime beween he effecive reiremen age and old-age pension eligibiliy. Again here is a link beween benefis and former wages. 9

11 componens. A firs one is relaed o he individual s earlier ne labor income. I is a fracion of his socalled pension base, i.e. a weighed average of revalued ne labor income in each of he hree acive periods of life. The ne replacemen rae is b 4a. The parameers p 1, p 2 and p represen he weighs aached o each period. This par of he pension rises in he individual s hours of work and his human capial h. I will be lower when he individual reires early (lower R ). Thanks o revaluaion, his par of he ne pension is adjused o increases in he overall sandard of living beween he ime ha workers build heir pension enilemens and he ime ha hey receive he pension. We assume ha pas earnings are revalued in line wih economy-wide wage growh x and hence follow pracice in many OECD counries (OECD, 2005; Whieford and Whiehouse, 2006). 6 The second componen of he pension is a fla-rae or basic pension. Every reiree receives he same amoun relaed o average ne labor income in he economy a he ime of reiremen. This assumpion assures ha also basic pensions rise in line wih produciviy. Here, he ne replacemen rae is b 4b. Fourh generaion individuals consume heir pension and he lump sum ransfer, as well as heir accumulaed wealh from he hird period plus ineres. They leave no debs, nor bequess. Subsiuing Equaions (2)-(4) for and (5)-(8) for ino Equaion (1), and maximizing wih respec o a,a,a,n,n,n ɶ,e and R, yields eigh firs order condiions for he opimal behavior of an agen enering he model a ime. Equaion (1) expresses he law of moion of opimal consumpion over ime. Equaions (14.a), (14.b) and (14.c) describe he opimal labor-leisure choice in each period of acive live. In each period, individuals supply labor up o he poin where he marginal uiliy of leisure equals he marginal uiliy gain from work. The laer consiss of wo pars. Working more hours in a paricular period raises addiional resources for consumpion boh in ha period and when reired. The marginal uiliy gain from work is higher when iniial consumpion is lower, and when an exra hour of work yields more exra consumpion. Higher human capial (and is underlying deerminans), lower axes on labor, lower axes on consumpion and lower nonemploymen benefis conribue o he gain from work. Exra consumpion during reiremen rises in he own-income-relaed pension replacemen rae (b 4a ), in he weigh aached o he relevan period when compuing he pension base (p j ), and in he revaluaion parameers. j+ 1 c j c ( 1 + j ) = β + r j=1, 2, (1) γ ( 1) ( τ )( ) ( τ ) ( τ ) ( τ ) 1 l1 w h b1 b4 a p1 w h1 1 1 x x + 1x + 2 = + β θ n1 c1 1+ c c4 1+ c l (14.a) 2 ( l 2 ) ( 1+ ( y )) ( 1 )( 1 ) γ l w ψ e,g,q h τ b θ n = 2 c2 ( 1+ τc ) ( 1+ ψ ( )) ( 1 τ ) b p w e,g,q h x x 2 + β c 4a y ( 1+ τ ) c (14.b) 6 We explain economy wide wage growh in Secion.. Individuals ake i as exogenous. 10

12 γ θ ɶ ( l ) n l ( 1+ ψ ( )) ( 1 τ ) ( 1 ) w e,g,q h R b = c + 2 y 1 a ( 1+ τ ) ( 1+ ψ ( )) R ( 1 τ ) b p w e,g,q h x + β c 4a + 2 y c ( 1+ τ ) c (14.c) Equaions (14.a)-(14.c) highligh posiive subsiuion effecs from he pension replacemen rae b 4a. To he exen ha higher replacemen raes raise individuals consumpion possibiliies (c j ), hey also cause adverse income effecs on labor supply. Basic pensions (b 4b ) do no direcly occur in Equaions (14), bu hey do affec employmen via his income effec. Equaion (15) describes he firs order condiion for he opimal effecive reiremen age. The LHS represens he uiliy loss from posponing reiremen. Laer reiremen reduces enjoyed leisure as early reiree, bu raises enjoyed leisure in beween periods of work for given work ime. The RHS shows he marginal uiliy gain from posponing reiremen. This marginal gain follows from consuming he exra labor income (vis-à-vis he early reiremen benefi) in he hird period, and he higher fuure old-age pension afer 65. The laer effec rises in b 4a and p. γ ( l ) θ l R ( 1 ( )) ( 1 ) ɶ ψ τ 1 ɶ ( ( )) ɶ 1 + ψ n ( 1 τ ) 4a + 2 y 1 4 ( 1+ τ ) 11 ( ( ) ) w + e,g,q h n + b n b + 2 y 1 a b = c ( 1+ τ c ) b p w e,g,q h + β c c Finally, equaion (16) imposes ha he marginal uiliy loss from invesing in human capial when young equals he oal discouned marginal uiliy gain in laer periods from having more human capial. Individuals will sudy more he higher fuure versus curren afer-ax real wages and he higher he marginal reurn of educaion o human capial ( ψ / e ). Labor axes during youh herefore encourage individuals o sudy, whereas labor axes in laer periods of acive life discourage hem. Noice also ha high benefi replacemen raes in laer periods (b 2, b a, b b ) and a high income-relaed pension replacemen rae (b 4a ), combined wih high weighs p 2 and p, will encourage young individuals o sudy. The reason is ha any fuure benefis and he fuure pension rise in fuure labor income, and herefore human capial. A final ineresing resul is ha young people sudy more all oher hings equal if hey expec o work harder in laer periods (n 2, n =R. ). x l1 1 c1 1 c2 2 1 c 1 c4 = β + β + β θ γ ( l ) e c e c e c e c e (16) c b ( ) wih: 1 1 w h1 1 τ 1 e 2 c e = ψ = 1+ τ c ( e,g y,q) w + 1h1 ( 1 τ 2 ) n2 + b2 ( 1 n2 ) e. 1+ τ c. (15)

13 c e ψ ( ) ( 1 ) ɶ e,g w + h R y,q τ ( 1 a a b ) n ( b ) + b b + b 2 1 b =. e 1+ τ c. 4 c e ( ) ( 1 τ ) e,g y,q 2 ψ = b 4a. e p n w h x 1+ τ j j + j 1 1 j + i 1 j= i= j c I will be obvious from he above discussion ha (for a given way of financing) he specific organizaion of pension benefis may have srong effecs on behavior in earlier periods of life. Boh income and subsiuion effecs occur. The laer are paricularly rich when pensions are linked o individuals own labor income. A higher replacemen rae b 4a raises he reurn o working (n) and building human capial (e, h) in earlier periods. Changes in he paricular weigh aached o hese earlier periods may modify hese incenive effecs. The reurn o educaion will rise in p 2 and p, bu fall in p 1. The reurn o working in he hird period will rise in p, ec. Policy makers may change all hese parameers. We invesigae he effecs of policy inervenions in Secion Producion of effecive human capial The specificaion and parameerizaion of he human capial producion funcion is ofen a problem in numerical endogenous growh models. In conras o goods producion funcions, here is no much empirical evidence and no consensus abou he deerminans of human capial growh, nor abou he underlying funcional form and parameer values (Bouzahzah e al, 2002, Arcalean and Schiopu, 2010). The lieraure shows a variey of funcions, ypically including one or wo of he following inpus: individual ime allocaed o educaion, privae expendiures on educaion by individuals hemselves or by heir parens, and governmen expendiures on educaion (e.g. Lucas, 1988, Glomm and Ravikumar, 1992; Docquier and Michel, 1999, Kaganovich and Zilcha, 1999; Bouzahzah e al., 2002; Fougère e al., 2009; Arcalean and Schiopu, 2010). In case of wo inpus, he adoped funcional form is very ofen Cobb-Douglas (e.g. Glomm and Ravikumar, 1992; Kaganovich and Zilcha, 1999; Docquier and Michel, 1999). Our specificaion also includes educaion ime of young individuals and educaion expendiures by he governmen. We see hese variables as indicaors for he quaniy of invesed privae and public resources. However, our specificaion is broader han his. Firs, we ake recen empirical evidence seriously ha he qualiy of educaion and he schooling sysem is very imporan (Hanushek and Woessmann, 2009). Beer qualiy implies higher cogniive skills for he same allocaion of resources. As a proxy for qualiy we will use OECD PISA science scores (see Secion 4.2 for furher discussion). As a second exension, our definiion of relevan (producive) governmen expendiures includes more han educaion. I also includes acive labor marke expendiures, public R&D expendiures and public fixed invesmen. This approach goes back o our use of he broader concep of effecive human capial. As in Dhon and Heylen (2009), effecive human capial (and worker produciviy) rise no only in accumulaed schooling or raining, bu also in he producive efficiency of accumulaed schooling. Educaion and acive labor marke expendiures direcly conribue o more human capial being accumulaed, public R&D and fixed invesmen expendiures will mainly raise he producive 12

14 efficiency of accumulaed human capial. The hypohesis ha public invesmen and infrasrucure services may also maer for aggregae human capial, nex o educaion expendiures, has been developed recenly by Agénor (2008). Equaion (17) shows our specificaion for he growh rae of effecive human capial. We adop a flexible CES-specificaion in educaion ime when young (e) and producive governmen expendiures in % of oupu (g y ). We add he qualiy of educaion (q) in a muliplicaive way. We allow q o vary across counries in laer secions. Nex o q we inroduce (consan, common) echnical parameers: φ is a posiive efficiency parameer, σ a scale parameer, v is a share parameer and κ he elasiciy of subsiuion. These parameers will be calibraed. 1 (1/ κ ) 1 (1/ κ ) ( y ) σκ /( κ 1) Ψ ( e, g, q) = φq ν g + (1 ν ) e (17) y Lack of exising empirical evidence makes an ex-ane assessmen of our specificaion very difficul. In previous work, however, we have been able o verify ha his specificaion performs beer han alernaive specificaions wihou qualiy, wih a narrower definiion of governmen expendiures or wih a differen funcional form (Heylen and Van de Kerckhove, 2010). In Secion 4 we show ha our model s predicions for educaion and per capia growh, which rely on (17), are fairly close o realiy for mos counries... Domesic firms, oupu and facor prices Firms ac compeiively on oupu and inpu markes and maximize profis. All firms are idenical. Toal domesic oupu is given by he producion funcion (18). Technology exhibis consan reurns o scale in aggregae physical capial (K ) and effecive labor (H ), so ha profis are zero in equilibrium. Equaion (19) describes oal effecive labor supplied by young, middle-aged and older workers. Noe our assumpions ha each generaion has size 1 and ha young workers inheri he 1 human capial of he middle-aged ( h1 = h 2 ). wih: Y 1 = K α H α (18) n H = n1 h1 + n2 h2 + n h = n1 + n2 + h (19) 1 x 1 1 ɶ 1 = 1 + and = x ψ(e,g y,q ) n R n, and where we use Equaions (9) and (10). Compeiive behavior implies in Equaion (20) ha firms carry physical capial o he poin where is afer-ax marginal produc ne of depreciaion equals he world real ineres rae (see also Backus e al., 2008). Physical capial depreciaes a rae δ k. Capial axes are source-based: he ax rae τ k applies o he counry in which he capial is used, regardless of who owns i. The real ineres rae being given, firms will insall more capial when he amoun of effecive labor increases or he capial ax rae falls. In ha case he ne reurn o invesmen in he home counry rises above he world ineres rae, and capial flows in. Furhermore, perfec compeiion implies equaliy beween he real wage and he marginal produc of effecive labor (Equaion 21). Higher real wages follow from an increase in physical capial per uni of effecive labor. Taking ino accoun (20), real wages per uni of effecive labor will herefore fall in he world real ineres rae and in domesic capial ax raes. 1

15 1 α H α δk ( 1 τ k ) = r K α K ( 1 α ) = w H (20) (21) Subsiuing (19) for H and (20) for K /H, we can rewrie (18) as α α / ( 1 α ) 2 α 1 τ k δk 1 τ k 1 K ( ) n Y = H = n + n + h. H r ( ) x If we finally recognize ha in seady sae r, τ k, x, e, and n j are consan, we obain he long-run (per capia) growh rae of he economy as 1 Y h 1 h 2 ln = ln ln ln ( e,g,q ) 1 = 1 = + Y 1 h1 h1 ( 1 ψ y ) (22) In line wih earlier models (e.g., Lucas, 1988; Azariadis and Drazen, 1990; Buier and Klezer, 199), he long-run (per capia) growh rae is posiively relaed o he qualiy of schooling (q) and o he fracion of ime ha young people allocae o educaion (e). I is also posiively relaed o he share of producive governmen expendiures (g y ), like in Barro (1990)..4. Governmen The governmen runs a balanced budge. Producive expendiures, consumpion, benefis relaed o non-employmen (including early reiremen benefis), old-age pension benefis, and lump sum ransfers a ime are financed by axes on labor, capial and consumpion. G y + Gc + B + PP + Z = Tn + Tk + T c (2) wih: G G y c = g Y y = g Y c 1 1 = τ τ 2 B (1 n e ) b w h (1 ) (1 n ) b w h (1 ) 2 2 ɶ R (1 n ) b w h (1 τ ) + (1 R ) b w h (1 τ ) j + 1 j ( + (1 τ )) + + ( (1 τ )) a b PP = b p w h n x b w h n 4a j j 4 j j j i 4 4b j j j j= 1 i= j j= 1 Z = 4z + 1 j + 1 j n = j j τ j j= 1 T n w h T T k = τ k [ αy δ K ] j c = τ c c j j= 1 14

16 Following Turnovsky (2000) and Dhon and Heylen (2009), we assume ha he governmen claims given fracions g y and g c of oupu for producive expendiures and consumpion. Non-employmen benefis (B ) are an uncondiional source of income suppor relaed o inaciviy ( leisure ) and nonmarke household aciviies. Alhough i may seem srange o have such ransfers in a model wihou involunary unemploymen, one can of course analyse heir employmen and growh effecs as a heoreical benchmark case (see also Rogerson, 2007; Dhon and Heylen, 2008, 2009). Moreover, here is also clear pracical relevance. Uncondiional or quasi uncondiional benefis o srucurally non-employed people are a fac of life in many European counries. We furher assume ha he pension sysem is fully inegraed ino he governmen accouns. We do no impose a specific financing of he PAYG pension plan, he governmen can use resources from he general budge o finance pensions. Finally, as we have menioned before, he governmen pays he same lump sum ransfer z o all individuals living a ime..5. Aggregae equilibrium and he curren accoun Opimal behavior by firms and households, and governmen spending for producive and consumpion purposes, underlie aggregae domesic demand for consumpion and invesmen goods in he economy. Our assumpion ha he economy is open implies ha aggregae domesic demand may differ from supply and income, which generaes inernaional capial flows and imbalance on he curren accoun. Equaion (24) describes aggregae equilibrium as i can be derived from Equaions (5)-(8), defined for all generaions living a ime, Equaions (18)-(21) and Equaion (2). In Equaion (24), F sands for ne foreign asses a he beginning of. The aggregae sock of wealh A accumulaes wealh held by individuals who enered he model in -1, -2 and -. Y + rf = C + I + Gc + Gy + CA (24) wih: F = A K CA = F F = A K I = K + δ K Parameerizaion and empirical relevance of he model The economic environmen described above allows us o simulae he ransiory and seady sae growh and employmen effecs of various changes in fiscal policy and he pension sysem. This simulaion exercise requires us firs o parameerize and solve he model. In Secion 4.1 we discuss our choice of preference and echnology parameers. Saring from acual cross-counry policy daa in Secion 4.2, we compare in Secion 4. our model s predicions wih he employmen and growh differences ha we have repored in Table 1. This comparison provides a firs and simple es of our model s empirical relevance. In Secion 5 we consider boh long-run equilibrium effecs and ransiional dynamics of policy changes. To solve he model and o perform our simulaions, we choose an algorihm ha preserves he non-linear naure of our model. We follow he mehodology basically proposed by Boucekkine (1995) and implemened by Juillard (1996) in he program Dynare. 15

17 4.1. Preference and echnology parameers Table 2 conains an overview of all parameers. Following among ohers Barro (1990), we se he rae of ime preference equal o 2% per year. Considering ha periods in our model consis of 15 years, his choice implies a discoun facor β equal o Wih respec o effecive labor, we assume a share coefficien 1-α equal o 0.7. This value is well in line wih he lieraure. For example, King and Rebelo (1990) also model goods producion as a funcion of effecive labor (human capial) and physical capial. They assume a value for 1-α equal o 2/. There is more conroversy in he lieraure abou he value of he ineremporal elasiciy of subsiuion in leisure (1/θ). Micro sudies ofen reveal very low elasiciies. However, given our macro focus, hese sudies may no be he mos relevan ones. Rogerson and Wallenius (2009) show ha micro and macro elasiciies may be unrelaed. Rogerson (2007) also adops a macro framework. He pus forward a reasonable range for θ from 1 o (Rogerson, 2007, p. 12). In line wih his, we impose θ o be equal o 2. The world real ineres rae is assumed consan in seady sae and equal o 4.25% per year. Considering a period of 15 years, his implies ha r = Finally, we se he physical capial depreciaion rae o 7.5% per year, which implies δ k = Our values for hese parameers are wihin he range of exising sudies. Table 2 Preference and echnology parameers Producion parameers (oupu) 1 α = 0.7 Effecive human capial producion φ = 4. 48, σ = 0. 99, v = , κ = Preference parameers β = 0.74, θ = 2, γ1 = 0.06, γ 2 = 0.125, γ = π = 0.5, ρ = 1.4, Ω = 2 World real ineres rae r = Physical capial depreciaion rae δ k = A second series of parameers have been deermined by calibraion: hree ase for leisure parameers (γ 1, γ 2, γ ) and wo parameers in he human capial producion funcion (he efficiency parameer φ and he scale parameer σ). We have calibraed hese parameers o Belgium. We choose his counry since in Belgium he calculaion of pension benefis fis exacly wihin he way we model i. Public pensions are proporional o average annual labor income earned over a period of 45 years, wih equal weighs o all years. There is no basic pension (OECD, 2005). In our model his comes down o b 4a >0, b 4b =0 and p 1 =p 2 =p =1/. The parameers γ 1, γ 2, γ, φ and σ have been deermined such ha wih observed levels of he policy variables (ax raes, benefi replacemen raes, pension replacemen rae, ec.) and he observed level of schooling qualiy (q) 7 in Belgium, he model correcly predics Belgium s employmen raes (n 1, n 2, n ), per capia growh rae, and educaion rae (e) in Underlying performance and policy daa are repored in Tables 1, and 4. We find ha he ase for leisure rises wih age (γ 1 =0.06, γ 2 =0.125, γ =0.189). Furhermore, we observe quasi consan reurns in human capial producion (σ 1). 7 And wih he values of wo parameers in he human capial producion funcion (v, κ) ha we discuss below (see also foonoe 8). 16

18 We had no ex ane indicaion on wo parameers in he human capial producion funcion: he share parameer v and he elasiciy of subsiuion parameer κ. We could assign sensible values o hese parameers hanks o a sensiiviy analysis on he resuls ha we repor in he nex secion. There we evaluae he capaciy of our model o explain six imporan macro variables in 1 OECD counries. Alhough he influence of v and κ on he explanaory power of our model is very limied, our guideline o pin down specific values for hese parameers (wihin a sensible range) was o minimize he deviaion of our model s predicions from he rue daa 8. This procedure implied v=0.125 and κ= The resul for κ reveals a higher degree of complemenariy beween privae educaion ime and governmen expendiures han in he Cobb-Douglas case. The resul for v demonsraes relaively high imporance for human capial formaion of privae educaion ime versus producive public expendiures. Neiher did we have an ex ane indicaion on he wo parameers in he composie leisure funcion in Equaion (4). We impose equal weigh for boh leisure ypes (π=0.5) and a sronger degree of subsiuabiliy han in he Cobb-Douglas case (ρ = 1.4). The specific value for ρ follows from a sensiiviy analysis on he predicions of our model for R and n (similar as in foonoe 8). An exensive robusness analysis reveals ha changes in hese parameers do no affec our resuls of he following secions in any imporan way. The normalisaion parameer Ω equals 2. The size of his parameer has no impac a all on our counry predicions or simulaion resuls Fiscal policy, pensions and educaion qualiy Tables and 4 describe key characerisics of fiscal policy and he pension sysem in /2004. Repored daa are averages of he available annual daa in ha period, unless indicaed oherwise. Our descripion of he daa here is shor. For some variables we provide more deail in Appendix 1. Our proxy for he ax rae on labor income concerns he oal ax wedge, for which we repor he marginal rae in %. The daa cover personal income axes, employee and employer social securiy conribuions payable on wage earnings and payroll axes. The OECD publishes hese ax daa for several family and income siuaions. Considering ha workers ypically earn less when hey are young (and have lower human capial) han when hey are middle-aged, we calculaed our τ 1 for each counry as an average of marginal ax raes for lower o middle income families. Tax raes for middle-aged and older workers were compued from OECD daa for middle o higher income families. As one can see in Table, however, differences wihin counries beween τ 1 on he one hand and τ 2 and τ on he oher, are very small. Cross-counry differences are much bigger. Belgium, Germany, Sweden and Finland have marginal labor ax raes above 55% or even 60%. The US and he UK have marginal labor ax raes below, or close o, 40%. Capial ax raes are effecive marginal corporae ax raes repored by he Insiue for Fiscal Sudies (heir EMTR, base case). Germany and Belgium have he highes raes. In conras o labor (and consumpion), capial is axed relaively lile in he Nordic counries. As o consumpion axes, we follow Dhon and Heylen (2009) in compuing hem as he raio of governmen indirec ax receips (ne of subsidies paid) o oal domesic demand ne of 8 From our model s predicions and he rue daa for 1 counries we compued for each variable (n 1, n 2, n, e, R, growh) he roo mean squared error normalized o he mean. We minimized he average normalized RMSE over all six variables. We hen adoped he following ieraive procedure. Given chosen values for v and κ we calibraed he efficiency parameer φ and he scale parameer σ. The values for v and κ had no influence on he calibraion resuls for γ j. Given he values for φ and σ, we checked wheher changes in v and κ could furher improve he model s explanaory power. New values for v and κ led o a recalibraion of σ and φ, ec. 17

19 indirec axes and subsidies. Our simplifying assumpion is ha consumpion ax raes correspond o aggregae indirec ax raes. The Nordic counries sand ou wih he highes consumpion ax raes, he US wih he lowes. Table Fiscal policy (Tax raes) ax rae on labor income when young (%) ax rae on labor income when middle age and older (in %) consumpion ax rae (%) ax rae on capial income (%) Proxy for : τ 1 τ 2, τ τ c τ k Ausria Belgium France Germany Ialy Neherlands Denmark Finland Norway Sweden UK US Canada Overall counry average Noe: Labor ax raes are daa for he oal ax wedge, marginal rae (OECD, Taxing Wages). Daa for For deails on he calculaion of ax raes by age group, see Appendix 1. Capial ax raes are effecive marginal corporae ax raes (Insiue for Fiscal Sudies, heir EMTR; daa for , see also Devereux e al., 2002). Consumpion ax rae: see Dhon and Heylen (2009). Daa for Table 4 summarizes our daa for he expendiure side of fiscal policy. A firs variable is our proxy for he ne non-employmen benefi replacemen rae b j (j = 1,2,a). Since in our model non-employmen is a srucural or equilibrium phenomenon, he daa ha we use concern ne ransfers received by srucurally or long-erm unemployed people. They include social assisance, family benefis and housing benefis in he 60 h monh of benefi receip. They also include unemploymen insurance or unemploymen assisance benefis if hese benefis are sill paid, i.e. if workers can be srucurally unemployed for more han five years wihou losing benefi eligibiliy 9. The daa are expressed in percen of afer-ax wages. In line wih our approach o deermine labor ax raes by age group, we are again guided by he same family and income cases o deermine b 1, b 2 and b a (see Appendix 1). Overall, he euro area and he Nordic counries pay he highes ne benefis on average. Transfers o srucurally non-employed people are by far he lowes in he US. A relaed variable is our proxy for he ne early reiremen benefi replacemen rae b b.the daa are again expressed in percen of afer-ax final wages. To assess he generosiy of early reiremen we inegrae he informaion available via b a and daa for he implici ax rae on coninued work in he early reiremen roue as provided by Duval (200) and Brand e al. (2005). For deails, see Appendix 1. We observe a very 9 This is he case in Ausria, Belgium, France, Germany, Finland, and he UK. Workers canno be srucurally non-employed and sill receive unemploymen benefis in he Neherlands, Ialy, Denmark, Norway and he US (OECD, 2004, Benefis and Wages, counry specific files). 18